Exaggeration, overstatement, hyperbole all mean an overstepping of the bounds of truth, especially in describing the goodness or badness or the greatness or the smallness of something.
Exaggeration does not always or even often imply dishonesty or an intent to deceive on the part of one making a statement, a representation, or a claim; it may merely imply an often temperamental unwillingness to be held down by the facts or a bias, whether favorable or unfavorable, so great that one cannot clearly see or accurately estimate the exact state of affairs depicted.
Unlike exaggeration , overstatement rarely carries any hint of depreciation; it is therefore often the term chosen by one desiring to stress the fact of exceeding the truth without any additional implications.
Hyperbole implies the use of exaggeration as a literary device. Though such use may arise from overpowering emotion, it more often suggests a desire to create a planned impression or particular effect; in either case hyperbole implies obvious extravagance in statement often producing a rhetorical effect that could not be gained otherwise.
Hyperbole is often used as the name of a figure of speech that produces its effect by overstatement as its opposite, litotes, does by understatement.